CN107465197B - Power distribution network reactive power optimization method based on dynamic multi-population particle swarm algorithm - Google Patents

Power distribution network reactive power optimization method based on dynamic multi-population particle swarm algorithm Download PDF

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CN107465197B
CN107465197B CN201710645678.9A CN201710645678A CN107465197B CN 107465197 B CN107465197 B CN 107465197B CN 201710645678 A CN201710645678 A CN 201710645678A CN 107465197 B CN107465197 B CN 107465197B
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particles
particle
population
reactive power
constraint
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CN107465197A (en
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王华芳
马宏忠
徐晗
顾苏雯
周昊
王春宁
许洪华
刘宝稳
吴书煜
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Nanjing Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Nanjing Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

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Abstract

The invention relates to a power distribution network reactive power optimization method based on a dynamic multi-population particle swarm algorithm, and belongs to the technical field of reactive power optimization control of power systems. The method comprises the following steps: 1) initializing a population and randomly generating a group of particle swarms, 2) dividing the particles according to a roulette algorithm to generate a plurality of subgroups; 3) updating the particles in the step 2) by using a speed and position updating formula, and judging the advantages and disadvantages of the updated particles and the particles before updating; 5) judging whether the particles reach the maximum iteration numbercIf yes, outputting an optimal result; if not, recording the current optimal particles as the optimal result; 6) judging whether the particles with the optimal results are changed after a is subjected to sub-optimization, if not, the optimal particles are the final results; if yes, go back to 2) to continue the optimization. The method of the invention solves the limitation of reactive power optimization problem under multi-constraint condition which can not be solved by the prior art, and the result of voltage reactive power optimization is better and the running speed is faster.

Description

Power distribution network reactive power optimization method based on dynamic multi-population particle swarm algorithm
Technical Field
The invention relates to a power distribution network reactive power optimization method based on a dynamic multi-population particle swarm algorithm, and belongs to the technical field of reactive power optimization control of power systems.
Background
The distribution network is an important link for distributing electric energy in an electric power system. With the rapid development of social economy, the system load is increased day by day, the topological circuit of the power distribution network is more complex, and the power grid loss is increased. The reasonable distribution of the reactive power of the power distribution network plays a crucial role in balancing the power flow distribution of the power distribution network, reducing the network loss of the power distribution network and stabilizing the voltage at the central load.
The particle swarm optimization is an optimization algorithm for processing a nonlinear optimization problem, belongs to one of evolutionary algorithms, and has the advantages of high convergence rate, simplicity in calculation, high precision, easiness in obtaining global optimum and the like. The method is widely applied to the aspects of signal processing, neural network training, reactive power optimization and the like. The basic particle swarm optimization aims at the problem of single-target or multi-target optimization without constraint conditions, and in practical application, the optimization targets often have the constraint conditions. Because the basic particle swarm algorithm is suitable for the optimization problem without constraint conditions, the search is blind, and the optimal solution meeting the constraint conditions is not easy to obtain. Therefore, the invention provides a dynamic multi-population particle swarm algorithm aiming at the constraint condition optimization problem.
The invention patent document with the application number of 201410222352.1 discloses a technical scheme named as a multi-target reactive power optimization method based on a self-adaptive chaotic particle swarm algorithm. The method solves the problem that the control variable possibly falls into a local optimal solution when the multi-objective reactive power optimization problem is processed, and reasonably solves the problem that the speed of solving the optimal value is too slow. However, the algorithm of the patent is complex and has limitations in processing the multi-constraint problem. Therefore, a method which can obtain the optimal solution of the voltage reactive power optimization problem in a short time and is more comprehensive when multiple constraint conditions are processed is needed, and the method can be widely applied to engineering practice.
Disclosure of Invention
The invention aims to solve the technical problem that aiming at the defects of the prior art, the invention provides the power distribution network reactive power optimization method which can obtain the optimal solution of the voltage reactive power optimization problem in a short time and is more comprehensive based on the dynamic multi-population particle swarm optimization algorithm when multi-constraint conditions are processed.
The technical scheme provided by the invention for solving the technical problems is as follows: a power distribution network reactive power optimization method based on a dynamic multi-population particle swarm algorithm executes the following steps:
step 1: initializing a population and randomly generating a group of particle swarms;
and calculating the fitness value f (x) of each particle and the degree value g of the violation of the constraint m by the node iim(x)，
Figure GDA0002464369510000021
L is the total number of closed branches in the distribution network;
Figure GDA0002464369510000022
network active loss for branch b;
gi1(x)＝Uimax-Ui；gi2(x)＝Ui-Uimin；gi3(x)＝Qimax-Qi；gi4(x)＝Qi-Qimin；
Figure GDA0002464369510000023
Uimin≤Ui≤Uimax；Qimin≤Qi≤Qimax；
Figure GDA0002464369510000024
Uiis the voltage of node i of the distribution network, UimaxUpper limit of node voltage amplitude, U, allowed for operation in distribution networkiminLower limit of node voltage amplitude, Q, allowed for operation of distribution networkiReactive power, Q, compensated for node iimaxSetting an upper limit, Q, for node i to compensate for reactive poweriminSetting a lower limit of compensation reactive power for a node i, wherein n is the number of load nodes and QsetAn upper limit for the total capacity of reactive compensation for a given distribution grid system;
step 2: calculating the degree q of violation of the constraint by each particle in the dynamic multi-populationmDividing the particles according to a roulette algorithm to generate a plurality of subgroups;
selecting optimized particles from the distributed subgroups through a strategy formula, wherein the strategy formula is as follows,
xsubswarm(u,m)＝ffind[ssort(Gmi(x),d)]
u-1, 2, …, k, k is the total number of subgroups; x is the number ofsubswarm(u, m) represents a particle in the u subgroup that optimizes the m constraint; ssort(Gmi(x) And d) represents a pair Gmi(x) Sorting from small to large, Gmi(x) Selecting G as the degree of the m-th constraint condition violation of the particles in the populationmi(x) D is a set value, and the size of the set value is smaller than the total number of particles in the subgroup; f. offindThe function is used for searching the position of the corresponding particle, so that the first d particles with smaller violation degree are selected;
and step 3: using velocity position update formula to optimize step 2Updating the speed and position of the particle, and calculating the fitness value f (x) of the updated particle and the degree value g violating the constraint condition mim(x)，
And comparing the quality of the updated particles with the quality of the particles before updating according to the quality judgment rule,
if the updated particle is superior, then
Figure GDA0002464369510000031
Otherwise
Figure GDA0002464369510000032
Wherein XjThe particle j is the particle after the t +1 time of updating;
after comparing the advantages and the disadvantages of the particles, seeking the region optimum in the subgroup according to the advantage and disadvantage judgment rule
Figure GDA0002464369510000033
And are combined with
Figure GDA0002464369510000034
Is relatively good or bad, if
Figure GDA0002464369510000035
Preferably, update
Figure GDA0002464369510000036
Is composed of
Figure GDA0002464369510000037
Otherwise
Figure GDA0002464369510000038
Still is
Figure GDA0002464369510000039
The velocity location update formula is used to update the velocity location,
Figure GDA00024643695100000310
Figure GDA00024643695100000311
and
Figure GDA00024643695100000312
respectively the speed and the position of the particle j in the e-dimensional space at the t +1 th iteration; c. C1、c2Taking a non-negative constant as an acceleration factor; r is1、r2Is between [0,1]Random positive real numbers in between;
Figure GDA00024643695100000313
finding the position of the optimal value of the individual in the e dimension for the particle j until the t iteration;
Figure GDA00024643695100000314
the position where the subgroup is optimal;
and 4, step 4: continuing to update the particles updated in the step 3, updating the R generation, and returning to the step 2 if the R generation is not updated;
and 5: and judging whether the particle reaches the maximum iteration time c, if so, outputting an optimal result, and if not, recording the current optimal particle as the optimal result.
Step 6: judging whether the particles with the optimal results are not changed after the sub-optimization a, if not, the particles with the optimal results are the final results; and if the change occurs, jumping to the step 2 to continuously optimize the particles.
The improvement of the technical scheme is as follows: grouping of roulette algorithms in step 2,
Figure GDA0002464369510000041
Figure GDA0002464369510000042
Gmi(x)＝{max{gmi(x),0},m＝1,2,...,5}；
wherein G ismi(x) To the extent that the particles in the population violate the mth constraint,xjis the jth particle in the population x, N is the total number of particles in the population, qm is the rate of the degree to which the particles violate each constraint,
Figure GDA0002464369510000043
for an arithmetic average of q1 to qm, gmi (x) is the mth inequality constraint.
The improvement of the technical scheme is as follows: the goodness determination rule in step 3,
1.fobj(a)＝fobj(b) 0 if f (x)a)＜f(xb) (ii) a The particles a are preferred; (xa) is the fitness value of the a particle, and f (xb) is the fitness value of the b particle;
2.fobj(a)＝fobj(b) if g is mim(xa)＜gim(xb)or(gim(xa)＝gim(xb)&&f(xa)＜f(xb) ); the particles a are preferred; gim (xa) is a degree value of violation of the constraint m of the a-particle, gim (xb) is a degree value of violation of the constraint m of the b-particle;
definition fobj(x) M, representing that the xth sub-group optimizes the mth constraint condition; f. ofobj(x) 0, denotes the x-th sub-group optimization objective function, i.e.
Figure GDA0002464369510000051
The invention adopts the technical scheme that the method has the beneficial effects that: in order to ensure that the voltage deviation degree meets the requirement of safe and stable operation of the system, a constraint condition of the voltage of each node needs to be set. In order to improve the economy of the reactive power compensation system and avoid excessive reactive power of the system, each load node and the total reactive power compensation capacity of the system have certain constraint.
In the basic particle swarm optimization, the flight speed of the particles is determined by the position of the individual optimum and the position of the global optimum, while in the dynamic multi-population particle swarm optimization, the flight speed of the particles is determined by the position of the individual optimum and the position of the subgroup optimum because the particles are divided into different subgroups.
Therefore, the limitation of the particle swarm optimization in solving the reactive power optimization problem under multiple constraint conditions is solved, and the result of voltage reactive power optimization performed by the dynamic particle swarm optimization is better and the running speed is higher.
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The invention will be further explained with reference to the drawings.
Fig. 1 is a schematic flow diagram of a power distribution network reactive power optimization method based on a dynamic multi-population particle swarm algorithm according to an embodiment of the present invention.
Figure 2 is a distribution line topology for a region in accordance with an embodiment of the present invention.
Detailed Description
Examples
In this embodiment, as shown in fig. 1, the method for power distribution network reactive power optimization based on a dynamic multi-population particle swarm algorithm includes the following steps:
step 1: initializing a population and randomly generating a group of particle swarms;
and calculating the fitness value f (x) of each particle and the degree value g of the violation of the constraint m by the node iim(x)，
Figure GDA0002464369510000061
L is the total number of closed branches in the distribution network;
Figure GDA0002464369510000062
for the network active loss of the branch b, the network loss can be directly obtained by utilizing a forward-backward flow-replacing tidal current calculation method;
when the reactive power optimization method of the power distribution network is processed by utilizing the dynamic multi-population particle swarm optimization, constraint conditions are set,
gi1(x)＝Uimax-Ui；gi2(x)＝Ui-Uimin；gi3(x)＝Qimax-Qi；gi4(x)＝Qi-Qimin；
Figure GDA0002464369510000063
in order to ensure that the voltage deviation degree meets the requirement of safe and stable operation of the system, a constraint condition of the voltage of each node needs to be set. In order to improve the economy of the reactive power compensation system and avoid excessive reactive power of the system, each load node and the total reactive power compensation capacity of the system have certain constraint. The constraints that the system needs to satisfy are as follows:
Uimin≤Ui≤Uimax；Qimin≤Qi≤Qimax；
Figure GDA0002464369510000064
Uiis the voltage of node i of the distribution network, UimaxUpper limit of node voltage amplitude, U, allowed for operation in distribution networkiminLower limit of node voltage amplitude, Q, allowed for operation of distribution networkiReactive power, Q, compensated for node iimaxSetting an upper limit, Q, for node i to compensate for reactive poweriminSetting a lower limit of compensation reactive power for a node i, wherein n is the number of load nodes and QsetAn upper limit for the total capacity of reactive compensation for a given distribution grid system;
the idea of a dynamic multi-population particle swarm algorithm is to dynamically group particles according to the ease of optimization for each constraint, i.e., each particle is arranged to optimize a constraint.
The same task of particles are arranged in the same subgroup, i.e. a subgroup optimizes a constraint condition correspondingly.
Step 2: to objectively reflect the degree of difficulty in optimizing a particle for different constraints, equation (10) defines the rate q of how well the particle violates each constraintm. For reflecting the difficulty of optimizing the particles for different constraints.
Calculating the degree q of each particle in the dynamic multi-population violating the constraint conditionmAnd the particles are divided into a plurality of subgroups according to a roulette algorithm, so that the particles are objectively and reasonably grouped.
The constraints that are difficult to optimize will have more subgroups to optimize according to roulette strategy. Definition fobj(x) M, denotes the x-th subgroup optimizationm constraints; f. ofobj(x) 0, denotes the x-th sub-group optimization objective function, i.e.
Figure GDA0002464369510000071
Since the particles that optimize each constraint are randomly assigned, the extent to which the particles violate the constraint also varies. To improve the optimizing capability of the population, the constraint m should be optimized by selecting particles with a smaller degree against the constraint m.
Selecting optimized particles from the distributed subgroups through a strategy formula, wherein the strategy formula is as follows,
xsubswarm(u,m)＝ffind[ssort(Gmi(x),d)]
u-1, 2, …, k, k is the total number of subgroups; x is the number ofsubswarm(u, m) represents the particle in the u subgroup that optimizes the m constraint; ssort(Gmi(x) And d) represents a pair Gmi(x) Sorting from small to large, Gmi(x) Selecting G as the degree of the m-th constraint condition violation of the particles in the populationmi(x) The first d elements, d being a set value, the size of which is smaller than the total number of particles in the subgroup (in the embodiment, half is selected as the value of d); f. offindThe function is used for searching the position of the corresponding particle, so that the first d particles with smaller violation degree are selected;
and step 3: in the basic particle swarm optimization, the flight speed of the particles is determined by the position of the individual optimum and the position of the global optimum, while in the dynamic multi-population particle swarm optimization, the flight speed of the particles is determined by the position of the individual optimum and the position of the subgroup optimum because the particles are divided into different subgroups.
Updating the speed and the position of the optimized particles in the step 2 by using a speed and position updating formula, and simultaneously calculating the fitness value f (x) of the updated particles and the degree value g violating the constraint condition mim(x)，
And comparing the quality of the updated particles with the quality of the particles before updating according to the quality judgment rule,
if the updated particle is superior, then
Figure GDA0002464369510000081
Otherwise
Figure GDA0002464369510000082
Wherein XjThe particle j is the particle after the t +1 time of updating;
after comparing the advantages and the disadvantages of the particles, seeking the region optimum in the subgroup according to the advantage and disadvantage judgment rule
Figure GDA0002464369510000083
And are combined with
Figure GDA0002464369510000084
Is relatively good or bad, if
Figure GDA0002464369510000085
Preferably, update
Figure GDA0002464369510000086
Is composed of
Figure GDA0002464369510000087
Otherwise
Figure GDA0002464369510000088
Still is
Figure GDA0002464369510000089
The velocity location update formula is used to update the velocity location,
Figure GDA00024643695100000810
in the voltage reactive power optimization problem, the total number of load nodes of the low-voltage distribution network is assumed to be N and Xi＝(xi1,xi2,···,xiN) Representing the reactive compensation capacity of each load node of the low-voltage distribution network, V, for the position information of the ith particlei＝(vi1,vi2,···,viN) The correction amount of the position information is represented as the velocity information of the ith particle.
Figure GDA00024643695100000811
And
Figure GDA00024643695100000812
respectively the speed and the position of the particle j in the e-dimensional space at the t +1 th iteration; c. C1、c2Taking a non-negative constant as an acceleration factor; r is1、r2Is between [0,1]Random positive real numbers in between;
Figure GDA00024643695100000813
finding the position of the optimal value of the individual in the e dimension for the particle j until the t iteration;
Figure GDA00024643695100000814
is the position where the subgroup is optimal.
Due to r1、r2For random positive real numbers, to ensure that the particle flight rate is an integer, the random result may be rounded.
And 4, step 4: continuing to update the particles updated in the step 3, updating the R generation, and returning to the step 2 if the R generation is not updated;
and 5: judging whether the particles reach the maximum iteration times c, if so, outputting an optimal result; if the maximum iteration times c are not reached, recording the current optimal particles as the optimal result.
Step 6: judging whether the particles with the optimal results are not changed after the sub-optimization a, if not, the particles with the optimal results are the final results; and if the change occurs, jumping to the step 2 to continuously optimize the particles.
The grouping of roulette algorithms in step 2 of the present embodiment,
Figure GDA0002464369510000091
Figure GDA0002464369510000092
Gmi(x)＝{max{gmi(x),0},m＝1,2,...,5}
wherein G ismi(x) To the extent that the particles in the population violate the mth constraint, xjIs the jth particle in the population x, N is the total number of particles in the population, qm is the rate of the degree to which the particles violate each constraint,
Figure GDA0002464369510000093
for an arithmetic average of q1 to qm, gmi (x) is the mth inequality constraint.
Since the particles need to complete the double optimization of the objective function and the constraint condition, and cannot judge the advantages or the disadvantages according to the size of the adaptive value, the following rules are set to judge the advantages or the disadvantages of the particles: the goodness determination rule in step 3,
1.fobj(a)＝fobj(b) 0 if f (x)a)＜f(xb) (ii) a The particles a are preferred; (xa) is the fitness value of the a particle, and f (xb) is the fitness value of the b particle;
2.fobj(a)＝fobj(b) if g is mim(xa)＜gim(xb)or(gim(xa)＝gim(xb)&&f(xa)＜f(xb) ); the particles a are preferred; gim (xa) is a degree value of violation of the constraint m of the a-particle, gim (xb) is a degree value of violation of the constraint m of the b-particle;
definition fobj(x) M, representing that the xth sub-group optimizes the mth constraint condition; f. ofobj(x) 0, denotes the x-th sub-group optimization objective function, i.e.
Figure GDA0002464369510000101
In order to show the superiority of the power distribution network reactive power optimization method based on the dynamic multi-population particle swarm algorithm in the embodiment, comparison is performed by combining actual cases. And carrying out voltage reactive comprehensive optimization analysis on a distribution line of a certain area. The line topology structure is shown in fig. 2.
The circuit has 11 nodes and 10 branches, and the branch 1 is S11-200 type distribution transformer with voltage regulation range of + -5 × 2.5.5% UNAt the moment, the on-load tap-changer of the transformer is 100 percent U at the middle 3 gearsNAnd (3) side. The power grid reference capacity is 200kVA, the voltage reference value of the high-voltage side of the transformer is 10kV, and the voltage reference value of the low-voltage side of the transformer is 380V. Node 1 is selected as a balance node, the voltage amplitude is 10.4kV, and the phase angle is 0. The specific parameters of the system are shown in table 1.
TABLE 1 System Branch parameters
Figure GDA0002464369510000102
Load flow calculation is carried out on the line by utilizing a forward-backward substitution method, the system network loss is 27.68kW, and the voltage result of each node is shown in Table 2.
TABLE 2 load flow calculation node voltages
Figure GDA0002464369510000111
From table 2, the node voltage at the end of the line is known to be within the normal range of the critical voltage. In order to meet the requirement of safe, economical and stable operation of the power system, the constraint conditions for setting the voltage reactive power optimization problem are as follows:
0.9≤Ui≤1.05
0≤Qi≤60kvar
Figure GDA0002464369510000112
comparing the result of the dynamic grouping particle swarm algorithm with the result obtained by the basic particle swarm algorithm, wherein the result is as follows:
TABLE 3 running speed and optimization results of different optimization algorithms
Figure GDA0002464369510000113
Figure GDA0002464369510000121
As can be seen from table 3, the network loss calculated by the dynamic multi-population particle swarm algorithm is high, but the minimum voltage is also high, and there is a great difference in the operation time, that is, the redundancy of the method in this embodiment is much smaller than that of the basic particle swarm algorithm.
It can be seen from the above table that the basic particle swarm algorithm cannot solve the problem with the constraint condition, and redundant computation of more than ten million times can be generated for obtaining the result meeting the constraint condition, so that the operation speed is greatly reduced, and the requirement on timeliness in the voltage reactive power optimization problem cannot be met.
The dynamic multi-population particle swarm algorithm, namely the method in the embodiment, has a wide application prospect in engineering practice because the algorithm is simple, the operation speed is high, convergence is easy, and the result of the voltage reactive power optimization problem can be obtained in a short time.
The present invention is not limited to the above-described embodiments. All technical solutions formed by equivalent substitutions fall within the protection scope of the claims of the present invention.

Claims (3)

1. A power distribution network reactive power optimization method based on a dynamic multi-population particle swarm algorithm is characterized by comprising the following steps:
step 1: initializing a population and randomly generating a group of particle swarms;
and calculating the fitness value f (x) of each particle in the particle swarm and the degree value g of the violation of the constraint m of the node iim(x)，
Figure FDA0002464369500000011
L is the total number of closed branches in the distribution network;
Figure FDA0002464369500000012
network active loss for branch b;
gi1(x)＝Uimax-Ui；gi2(x)＝Ui-Uimin；gi3(x)＝Qimax-Qi；gi4(x)＝Qi-Qimin；
Figure FDA0002464369500000013
Uimin≤Ui≤Uimax；Qimin≤Qi≤Qimax；
Figure FDA0002464369500000014
Uiis the voltage of node i of the distribution network, UimaxUpper limit of node voltage amplitude, U, allowed for operation in distribution networkiminLower limit of node voltage amplitude, Q, allowed for operation of distribution networkiReactive power, Q, compensated for node iimaxSetting an upper limit, Q, for node i to compensate for reactive poweriminSetting a lower limit of compensation reactive power for a node i, wherein n is the number of load nodes and QsetAn upper limit for the total capacity of reactive compensation for a given distribution grid system;
step 2: calculating the degree q of violation of the constraint by each particle in the dynamic multi-populationmDividing the particles according to a roulette algorithm to generate a plurality of subgroups;
selecting optimized particles from the distributed subgroups through a strategy formula, wherein the strategy formula is as follows,
xsubswarm(u,m)＝ffind[ssort(Gmi(x),d)]
u-1, 2, …, k, k is the total number of subgroups; x is the number ofsubswarm(u, m) represents a particle in the u subgroup that optimizes the m constraint; ssort(Gmi(x) And d) represents a pair Gmi(x) Sorting from small to large, Gmi(x) Selecting G as the degree of the m-th constraint condition violation of the particles in the populationmi(x) D is a set value, and the size of the set value is smaller than the total number of particles in the subgroup; f. offindThe function is used for searching the position of the corresponding particle, so that the first d particles with smaller violation degree are selected;
and step 3: using velocity position update formula to optimize step 2Updating the speed and position of the particle, and calculating the fitness value f (x) of the updated particle and the degree value g violating the constraint condition mim(x)，
And comparing the quality of the updated particles with the quality of the particles before updating according to the quality judgment rule,
if the updated particle is superior, then
Figure FDA0002464369500000021
Otherwise
Figure FDA0002464369500000022
Wherein XjThe particle j is the particle after the t +1 time of updating;
after comparing the advantages and the disadvantages of the particles, seeking the region optimum in the subgroup according to the advantage and disadvantage judgment rule
Figure FDA0002464369500000023
And are combined with
Figure FDA0002464369500000024
Is relatively good or bad, if
Figure FDA0002464369500000025
Preferably, update
Figure FDA0002464369500000026
Is composed of
Figure FDA0002464369500000027
Otherwise
Figure FDA0002464369500000028
Still is
Figure FDA0002464369500000029
The velocity location update formula is used to update the velocity location,
Figure FDA00024643695000000210
Figure FDA00024643695000000211
and
Figure FDA00024643695000000212
respectively the speed and the position of the particle j in the e-dimensional space at the t +1 th iteration; c. C1、c2Taking a non-negative constant as an acceleration factor; r is1、r2Is between [0,1]Random positive real numbers in between;
Figure FDA00024643695000000213
finding the position of the optimal value of the individual in the e dimension for the particle j until the t iteration;
Figure FDA00024643695000000214
the position where the subgroup is optimal;
and 4, step 4: continuing to update the particles updated in the step 3, updating the R generation, and returning to the step 2 if the R generation is not updated;
and 5: judging whether the particles reach the maximum iteration times c, if so, outputting an optimal result; if the maximum iteration times c are not reached, recording the current optimal particles as the optimal result;
step 6: judging whether the optimal particles are not changed after the optimal particles are subjected to the a sub-optimization, and if the optimal particles are not changed, determining the optimal particles as a final result; and if the change occurs, jumping to the step 2 to continue the optimization.
2. The power distribution network reactive power optimization method based on the dynamic multi-population particle swarm algorithm according to claim 1, wherein the method comprises the following steps: grouping of roulette algorithms in step 2,
Figure FDA0002464369500000031
Figure FDA0002464369500000032
Gmi(x)＝{max{gmi(x),0},m＝1,2,...,5}；
wherein G ismi(x) To the extent that the particles in the population violate the mth constraint, xjIs the jth particle in the population x, N is the total number of particles in the population, qm is the rate of the degree to which the particles violate each constraint,
Figure FDA0002464369500000033
for an arithmetic average of q1 to qm, gmi (x) is the mth inequality constraint.
3. The power distribution network reactive power optimization method based on the dynamic multi-population particle swarm algorithm according to claim 1, wherein the method comprises the following steps: the goodness determination rule in step 3,
1.fobj(a)＝fobj(b) 0 if f (x)a)＜f(xb) (ii) a The particles a are preferred; (xa) is the fitness value of the a particle, and f (xb) is the fitness value of the b particle;
2.fobj(a)＝fobj(b) if g is mim(xa)＜gim(xb)or(gim(xa)＝gim(xb)&&f(xa)＜f(xb) ); the particles a are preferred; gim (xa) is a degree value of violation of the constraint m of the a-particle, gim (xb) is a degree value of violation of the constraint m of the b-particle;
definition fobj(x) M, representing that the xth sub-group optimizes the mth constraint condition; f. ofobj(x) 0, denotes the x-th sub-group optimization objective function, i.e.
Figure FDA0002464369500000041
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